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begin quote ita"
CHAPTER I [:] Notions from Set Theory [...] 4. FINITE AND INFINITE SETS. "end quote
These pages can stand alone but it is best to have the book.    
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Please read these notes from the beginning to here and then paragraph 5 of 4.

SEQUENCES

Before reading this page, please have another look at reading   I 4 2 .

begin quote ita-1-4-5-pg11 "
The set of natural numbers can be used to give an easy definition of the notion of a sequence. A   sequence of n elements in a set X,   or an   n-tuple of elements of X,   may be defined to be a function from   {1,2,...,n}   into   X;   if the function is denoted   f   and we write   f(1)=x,   f(2)=x,   ...   f(n)=x,   then the   n-tuple   is often written   (x,x,...,x).   An   infinite sequence of elements of X   (or a   sequence of elements of X   if there isn't any danger of confusion with finite sequences) is a function from the set of all natural numbers into   X;   as above this can be written   (x,x,x,...),   or, more conventionally,   x,x,x,...   or sometimes   .
"end quote

on to Chapter II